Abstract
Anyone who has taken first-semester calculus has spent a considerable amount of time studying polynomial functions and their graphs. Calculus I students typically learn how to locate certain special points with respect to the graphs of polynomials, such as their x- and y-intercepts, their local maxima and minima, and their points of inflection (if any). They then learn that these points, together with information provided by the first and second derivatives of the functions, can be used to sketch the graphs of polynomials.
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